Abstract
This article gives a basic introduction to the principles of Bayesian inference in a machine learning context, with an emphasis on the importance of marginalisation for dealing with uncertainty. We begin by illustrating concepts via a simple regression task before relating ideas to practical, contemporary, techniques with a description of ‘sparse Bayesian’ models and the ‘relevance vector machine’.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Jaynes, E.T.: Probability theory: the logic of science. Cambridge University Press, Cambridge (2003)
Evans, M., Swartz, T.B.: Methods for approximating integrals in statistics with special emphasis on Bayesian integration. Statistical Science 10, 254–272 (1995)
Beal, M., Ghahramani, Z.: The Variational Bayes web site at (2003), http://www.variational-bayes.org/
Bishop, C.M., Tipping, M.E.: Variational relevance vector machines. In: Boutilier, C., Goldszmidt, M. (eds.) Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence, pp. 46–53. Morgan Kaufmann, San Francisco (2000)
Neal, R.M.: Bayesian Learning for Neural Networks. Springer, Heidelberg (1996)
Berger, J.O.: Statistical decision theory and Bayesian analysis, 2nd edn. Springer, Heidelberg (1985)
MacKay, D.J.C.: The evidence framework applied to classification networks. Neural Computation 4, 720–736 (1992)
Williams, P.M.: Bayesian regularisation and pruning using a Laplace prior. Neural Computation 7, 117–143 (1995)
Tipping, M.E.: Sparse Bayesian learning and the relevance vector machine. Journal of Machine Learing Research 1, 211–244 (2001)
Tipping, M.E., Faul, A.C.: Fast marginal likelihood maximisation for sparse Bayesian models. In: Bishop, C.M., Frey, B.J. (eds.) Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics, Key West, FL, January 3-6 (2003)
MacKay, D.J.C.: Bayesian interpolation. Neural Computation 4, 415–447 (1992)
Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)
Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. Chapman and Hall, Boca Raton (1995)
MacKay, D.J.C.: Information Theory, Inference and Learning Algorithms. Cambridge University Press, Cambridge (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Tipping, M.E. (2004). Bayesian Inference: An Introduction to Principles and Practice in Machine Learning. In: Bousquet, O., von Luxburg, U., Rätsch, G. (eds) Advanced Lectures on Machine Learning. ML 2003. Lecture Notes in Computer Science(), vol 3176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28650-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-28650-9_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23122-6
Online ISBN: 978-3-540-28650-9
eBook Packages: Springer Book Archive